Insurers including Radian Group Inc. and MGIC Investment Corp. that within the past year debt traders viewed as likely to default, are positioning themselves for growth as lawmakers and regulators consider shifting housing risk from the government to private capital. In the Senate, the senior Republican and the Democratic chairman of the banking committee have pledged to work together to shrink FHA’s role, as the insurers lobby to level the playing field with the government.

“What we’re really looking for is at least parity with FHA, so FHA isn’t more dominant in the marketplace,” Teresa Bryce Bazemore, president of Philadelphia-based Radian’s main insurance unit, said in an interview in Washington after testifying on Feb. 28 at a Senate hearing on the agency’s financial problems. “I don’t think you can ever expect a government agency to be as nimble as a private entity.”

Mortgage insurers have rallied this year on bets the companies can continue to increase sales as the U.S. scales back. MGIC, based in Milwaukee, has rallied 85% since December. Radian is up 53% and Genworth Financial Inc., which also offers life insurance and long-term care coverage, advanced 28%.

The firms are poised to make further gains in market share as FHA is set to increase the annual cost of insuring loans by another 10 basis points as of April 1.

Private guarantors wrote new policies on $175 billion in mortgages in 2012, more than double the year before, according to data from newsletter Inside Mortgage Finance. The industry currently insures about $900 billion in loans, while FHA’s portfolio is $1.1 trillion.

Investors have increasingly been betting on mortgage insurance as the housing market recovers. Arch Capital Group Ltd. said Feb. 8 it reached a $300 million deal to enter the mortgage guaranty business by acquiring assets from bankrupt insurer PMI Group Inc. New insurer NMI Holdings Inc. raised $550 million in private capital last year to back home loans.

“We are extremely pleased to be able to provide a strong source of private capital to a U.S. mortgage insurance market in great need of capacity,” Constantine Iordanou, chief executive officer of Arch, said in a statement announcing the deal. Arch will benefit from “significant opportunities in the U.S. mortgage insurance marketplace,” he said.

MGIC said yesterday it raised about $1.1 billion selling stock and notes. It fell 12% to $4.92 at 4:15 p.m. in New York trading after rising from 84 cents in August. Radian, which raised $689 million last week, fell 5.6% to $9.37. It’s rallied from $2.02 in May.

“It’s a bet on housing, but it’s also a bet on a return to normalcy in the mortgage market,” said Jasper Burch, an analyst at Macquarie Group Ltd. “The new business that these guys are writing is well above historical standards.”

Mortgage guarantors are working in Washington to ensure their voices are heard as regulators and lawmakers craft policies that could sustain their industry’s recent gains. Bazemore and other executives will be back on Capitol Hill March 13, testifying at a hearing in the Republican-led House of Representatives billed as a look at “the competitive advantages the FHA has relative to private mortgage insurers and how those advantages contribute to the crowding out of private capital in housing finance.”

The mortgage insurance business “is at a crossroads,” said Basel Petrou, managing partner of Federal Financial Analytics Inc., a Washington-based consultant to financial services companies. “In terms of those companies with legacy books, they are turning the corner in terms of their operations, and there are new entrants in the market, so the concept of private insurance as a viable alternative continues and should go forward.”

To be sure, the industry is struggling amid losses on policies sold prior to the housing crash. MGIC hasn’t reported a yearly profit since 2006. Radian Group recorded losses in five of the past six years.

PMI Group filed for bankruptcy protection in November 2011 after the Arizona Department of Insurance took over the main unit as claims on soured mortgages drained capital. Triad Guaranty Inc. also had to stop selling new policies when capital ran short, and Old Republic International Corp. has scaled back from the market.

Essent Guaranty Inc., a new mortgage insurer whose backers include Goldman Sachs Group Inc., later bought assets from Triad and began writing policies in 2011. Genworth announced plans in January to distance its unprofitable mortgage insurer from units that sell life insurance and long-term care coverage. The move may also allow outside investors to bet directly on the guaranty business, Richmond, Virginia-based Genworth said at the time.

The losses the industry suffered as a result of the crisis show private mortgage insurance was working as it was designed, said Clifford Rossi, a former risk manager and managing director at Citigroup Inc. who now teaches at the University of Maryland’s Robert H. Smith School of Business.

“The last companies still standing may have a very compelling argument that here you had an industry that did it exactly the way you would think private capital should be designed,” Rossi said in an interview. Some “companies went out of business and there was not a taxpayer dollar that subsidized them.”

Opportunities for mortgage insurers are already growing as FHA raises the premiums it charges borrowers to insure their loans in a bid to offset its losses. The agency’s market share dropped to 43% last year from the peak of 71% in 2009 after a series of premium increases, according to Inside Mortgage Finance.